Method and apparatus for extracting surface from three-dimensional shape data as well as recording medium

ABSTRACT

The apparatus sets a standard surface or a standard line with respect to three-dimensional shape data comprising polygons representing an object in a space where the three-dimensional shape data exist, extracts from the three-dimensional shape data polygons having inclination angles with respect to the set standard surface or the set standard line in a predetermined range, and set each collection of the extracted polygons as an extracted surface. Further, the apparatus displays each of the collection of extracted polygons as a surface on a display with putting a color or pattern to each of the collection of the polygons extracted correspondingly to one of the set inclination angles that is different from those of other collections of polygons.

[0001] This application is based on Japanese Patent Application No.2000-279219 filed on Sep. 14, 2000, the contents of which are herebyincorporated by reference.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to a method for extracting asurface from three-dimensional shape data, an apparatus for extracting asurface from three-dimensional shape data and a recording medium whichstores a program for the same.

[0004] 2. Description of the Prior Art

[0005] Conventionally, three-dimensional shape data of a component isused for examining its size and finish precision.

[0006] For example, there has been proposed an apparatus that candisplay three-dimensional shape image of a component on a display andcalculate distances between a specific surface and a specific pointdesignated by a user to display the calculation results. A problemdetected with this method is that the surface appointed by the user isin fact a polygon comprised in the surface and, therefore, the distancescalculated based on the polygon is variable depending on an angle of thepolygon. A surface generally comprises a collection of polygons;however, orientations of the polygons are non-uniform.

[0007] Elements such as a surface, a cylinder and the like may beextracted from three-dimensional data of a component by comparing thethree-dimensional data with CAD data of the same component. A sideforming an outline of the component is then extracted based on theextracted elements. Distances between the extracted elements and theside are calculated, and the calculated values are compared with designvalues.

[0008] Various three-dimensional measurement devices of non-contact typeor contact type may be used for obtaining three-dimensional shape dataof a component.

[0009] In the above-described conventional method, CAD data of acomponent is used for extracting a surface and a side of the component.Accordingly, in the absence of the CAD data, user's workload isincreased since the user has to manually extract the surface or the likeby selecting an appropriate area of three-dimensional data by, forexample, visual observation thereof.

[0010] In some cases, a user may need to know types of surfacescomprised in three-dimensional data, orientations of the surfaces and soon. In such cases, a normal line of each of polygons (polygon surfaces)that are comprised in the three-dimensional shape data is displayed as asegment or a vector.

[0011] Above method is suitable for detecting an orientation of apolygon; however, the method is insufficient for detecting anorientation and a condition of a surface as an outline of a componentcomprising a collection of polygons. Further, since information of allthe polygon surfaces is displayed in the method, the method is timeconsuming for a user who desires to selectively obtain necessaryinformation of the surfaces.

[0012] Japanese Unexamined Patent Publication No. 10-162167 discloses amethod wherein plotted three-dimensional coordinates are displayed on adisplay as a rectangular parallelepiped, and xy surface, yz surface andzx surface are displayed with being put different colors or patterns.This method improves visibility in the visual direction; however, it isinsufficient for detecting directions of every surfaces of an object.

[0013] Three-dimensional shape data subjected to modeling of athree-dimensional measurement device typically include noise caused bysurface characteristics, colors of surfaces or a shape of an object.Especially, such noise is increased in the vicinity of an edge of theobject, thereby making it difficult to grasp the shape of the object.

SUMMARY OF THE INVENTION

[0014] The present invention is accomplished by considering aboveproblems. The invention enables to extract a surface of an object fromthree-dimensional shape data without using CAD data or the like. Anobject of the invention is to facilitate comprehension of not only thesurface but also a shape of the object.

[0015] A method according to one aspect of the present inventioncomprises; setting a standard surface or a standard line with respect tothree-dimensional shape data comprising polygons representing an objectin a space where the three-dimensional shape data exist; extractingpolygons each having an inclination angle in a predetermined range; andsetting the polygons as an extracted surface.

[0016] An apparatus according to another aspect of the present inventioncomprises a setting portion for setting, with respect tothree-dimensional data comprising polygons representing an object, astandard surface or a standard line in a space where thethree-dimensional data exist; an angle setting portion for setting arange of inclination angles of polygons with respect to the standardsurface or the standard line; an designating portion for designating anallowable range in the inclination angles; a calculating portion forcalculating angles made by the polygons and the standard surface or thestandard line; and an extracting portion for extracting polygons eachhaving an inclination angle in the allowable range of the inclinationangles. Here, each of the portions may be independent of each other andthe two portions or more may be comprised of a common resource.

[0017] The apparatus further comprises a standard element calculatingportion for detecting a standard element which is a surface or a linethat is in a specific positional relationship with the standard surfaceor the polygons. A normal line may preferably be used as the line of thestandard element. For example, it is judged whether or not an angle madeby two normal lines is in the allowable range. Here, each of theportions may be independent of each other and the two portions or moremay be comprised of a common resource.

[0018] The recording medium according to further aspect of the presentinvention records a program for letting a computer execute theprocessing of: setting a standard surface or a standard line withrespect to three-dimensional shape data comprising polygons representingan object in a space where the three-dimensional shape data exist;extracting polygons each having an inclination angle with respect to thestandard surface or a referenced line in a predetermined range; anddesignating a collection of the extracted polygons as an extractedsurface.

BRIEF DESCRIPTION OF THE DRAWINGS

[0019]FIG. 1 is a block diagram showing a structure of a data processingapparatus according to an embodiment of the present invention.

[0020]FIG. 2 is a block diagram showing functions to be realized by theapparatus.

[0021]FIG. 3 is a perspective view showing an example of an object.

[0022]FIG. 4 shows polygon data of the object.

[0023]FIG. 5 shows examples of a standard surface and a standard lineset in the polygon data.

[0024]FIG. 6 shows an extracted surface on which is put a color.

[0025]FIG. 7 shows extracted surfaces sorted into groups on which areput different colors.

[0026]FIG. 8 shows surfaces displayed together with their sizes.

[0027]FIG. 9 is an example of a cross-section of a polygon.

[0028]FIG. 10 shows relationship between a standard surface and asurface to be extracted.

[0029]FIG. 11 illustrates a method of eliminating noise.

[0030]FIG. 12 shows an example of sectional shape data.

[0031]FIG. 13 shows an example of a segment extracted from the sectionalshape data.

[0032]FIG. 14 is an example of segments composing a line.

[0033]FIG. 15 illustrates a method of eliminating noise.

[0034]FIG. 16 is a flow chart showing a flow of processing carried outby the data processing apparatus.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0035]FIG. 1 is a block diagram showing a structure of a data processingapparatus 1 according to an embodiment of the present invention.

[0036] Referring to FIG. 1, the data processing apparatus 1 is comprisedof an apparatus body 11, a display 12, a keyboard 13, a mouse 14 and soon. The apparatus body 11 comprises a CPU, a ROM, a RAM, a magnetic diskdevice, a magneto-optical disk device, a CD-ROM drive, a floppy diskdrive and so on. The CPU serves to execute programs memorized in the ROMor the RAM and realizes various functions to be described later in thisspecification. The programs are recorded in a recording medium MA suchas a CD-ROM and a floppy disk and can be installed in the magnetic discdevice to be loaded on the RAM when so required. It is also possible todownload the programs from other servers via a network not shown.

[0037] On a display screen HG of the display device 12, there aredisplayed three-dimensional data DT that are input into the apparatus,three-dimensional shape data that are subjected to a predeterminedprocessing in the apparatus body 11, other various data, images based onthe data and so on.

[0038] The keyboard 13 and the mouse 14 are used when a user gives acommand to or inputs data into the apparatus body 11.

[0039] The three-dimensional measurement device 15 obtains threedimensional shape data DT of an object Q by the non-contact type methodsuch as the light-section method or the contact type method. Thethree-dimensional data DT output from the three-dimensional measurementdevice 15 are polygon data (polygon model) MR comprising polygons. Inthe case where distance data are output from the three-dimensionalmeasurement device 15, the distance data are converted into the polygondata MR in the apparatus body 11.

[0040]FIG. 2 is a block diagram showing a function realized in theapparatus body 11.

[0041] Referring to FIG. 2, the apparatus body 11 comprises a standardsurface setting portion 21, an inclination angle setting portion 22, anallowable angle designating portion 23, a color-designating portion 24,a selection designating portion 25, a cross-section extracting portion26, a normal line calculating portion 27, an extracting portion 28, asorting and grouping portion 29, a display processing portion 30,memorizing areas AR1 and AR2 and so on. As a matter of convenience, FIG.2 separately shows each of the portions for each function of theapparatus body 11; however, each of the portions is not alwaysindependent of each other. Functions in the plural portions may berealized by a single element or software. Alternatively, a function inone of the portions may be realized in cooperation with the pluralelements or the software. For example, a case in which each of theportions corresponds to each of steps carried out by using the softwareis included.

[0042] The memorizing areas AR1 and AR2 are predetermined areas providedin the RAM or the like of the apparatus body 11. The polygon data MR arememorized in the memorizing area AR1. The polygon data MR include, forexample, coordinate data of each of vertexes of the polygons, dataindicating front side or back side of each of surfaces of the polygonsand so on. The front or back side of the surface is designated by, forexample, order of the vertex coordinates. In turn, the memorizing areaAR2 memorizes extracted surfaces T and lines S, generatedthree-dimensional shape data DT and sectional shape data DK and so on.

[0043] In the example shown in FIG. 4, an image HG1 based on the polygondata MR is displayed on a screen. The polygon data MR are obtained bymeasuring the object Q of FIG. 3 using the three-dimensional measurementdevice 15. The polygon data MR have surfaces (virtual surfaces) P1 toP12 comprising multiple polygons PG. The surfaces P1 to P12 respectivelycorresponds to outline surfaces K1 to K12 of the object Q.

[0044] As shown in FIG. 9, the surface P1 is composed of multiplepolygons PG1, PG2, PG3 and so on. The polygons are different in anglesfrom one another, i.e. directions of normal lines of the polygons aredifferent from one another.

[0045] In the example shown in FIG. 12, an image HG6 of sectional shapedata DK is displayed on a screen. The sectional shape data DK areprepared by cutting the polygon data MR shown in FIG. 4 along ahorizontal plane crossing the center of the polygon data MR. Thesectional shape data DK have lines (virtual lines) S1 to S12 comprisingmultiple segments SB.

[0046] As shown in FIG. 14, the line S1 is composed of the multiplesegments SB1, SB2, SB3, etc. The segments are different in angles fromone another, i.e. directions of the segments are different from oneanother.

[0047] The standard surface setting portion 21, the inclination anglesetting portion 22, the allowable angle designating portion 23, thecolor designating portion 24 and the selection designating portion 25each serves to set or designate relevant positions or values dependingon contents of operation performed by the user using the keyboard 13 andthe mouse 14.

[0048] The standard surface setting portion 21 sets a standard surfaceRM or a standard line RS with respect to polygon data MR in a spacewhere the polygon data MR exist. Generally, a surface lying in parallelwith any one of the surfaces P of the polygon data MR is set as thestandard surface RM. Especially, a surface that is a standard formeasurement is selected as the standard surface RM for the processing ofor for the reproduction of the object Q. Generally, a ridgeline betweensurfaces P of the polygon data MR is set as the standard line RS. Acenterline that passes through an opening of the object Q or the likemay be set as the standard line.

[0049] The standard line RS may be set with respect to sectional shapedata DK in a space where the sectional shape data DK exist.

[0050] In the example shown in FIG. 5, polygon data MR are displayed onthe display as an image HG2, and the standard surface RM and thestandard line RS are to be set on the image. A surface close to thesurface P11, i.e. a bottom surface, is set as the standard surface RM. Aline close to a ridgeline on boundary between the surface P11 and thesurface P1 is set as the standard line RS.

[0051] In the example shown in FIG. 12, an image HG6 representing thesectional shape data DK is displayed, and the standard line RS is to beset on the image HG6. A line in parallel with the line S1 is set as thestandard line RS.

[0052] For setting the standard surface RM and the standard line RS,known application programs or methods may be used. For example, adirectional vector of the standard line RS is input by using thekeyboard 13 in order to set the standard line RS. A normal line vectorof the standard surface RM and a coordinate of a point on the standardsurface RM are input by using the keyboard 13. Also, a surface comprisedin a shape model may be selected as the standard surface RM.

[0053] The inclination angle setting portion 22 sets inclination anglesθ made by polygons PG to be extracted and the normal line HS of thestandard surface RM or the standard line RS. The inclination angles θare selected from the range of 0 degree to 180 degrees (0 to π). Inother words, a surface is not distinguished in terms of back side orfront side and, therefore, surfaces that are in parallel to one anotherare extracted simultaneously irrespective of which side of each of thesurfaces is used for setting the inclination angles θ. Accordingly, itis necessary to prepare data indicating back or front of a surface inorder to distinguish the front side surface from the back side surface.The inclination angles θ may be set by, for example, inputting a valuecorresponding to each of the inclination angle θ using the keyboard 13.

[0054] The allowable angle designating portion 23 designates anallowable angle δ. The allowable angle δ indicates an allowable range ±δwith respect to the set inclination angles θ. The allowable angle δ isset in such a manner as 0.5 degree, 1 degree and 5 degree, for example.

[0055] The color designating portion 24 designates a color or a patternwhen displaying an extracted surface T. For example, a color or apattern of a surface T extracted correspondingly to one of the setinclination angles θ is assigned so that the color or the pattern isdifferent from that of other surfaces T. Also, the color or the patternis differed according to groups of extracted surfaces T.

[0056] The selection designating portion 25 designates a selectionwhether or not the extracted surface T is to be displayed. For example,the designation is performed with respect to each of the extractedsurfaces T that are extracted correspondingly to one of the setinclination angles θ or with respect to each of the groups of theextracted surfaces T.

[0057] The cross-section extracting portion 26 calculates sectionalshape data DK indicating a shape of a cross-section of an object Q basedon polygon data MR. The sectional shape data DK are comprised bysegments SB indicating an outline of the cross-section.

[0058] The normal line calculating portion 27 detects a normal line HSwith respect to a standard surface RM or a polygon PG.

[0059] The extraction portion comprises a polygon extracting portion281, a segment extracting portion 282 and a noise eliminating portion283.

[0060] The polygon extracting portion 281 calculates angles α made bythe normal line HS of the standard surface RM and the normal lines HS ofthe polygons PG. The polygon extracting portion 281 judges whether ornot each of the calculated angles α is in the allowable angle range ±δof the set inclination angles θ to extract polygons in an inclinationangle range θ±δ.

[0061] As shown in FIG. 10, the polygon PG is extracted when the anglemade by the normal line HSRr of the standard surface RM and the normalline HSp of the polygon PG is in the inclination angle range θ±δ.

[0062] With respect to sectional shape data DK calculated by thecross-section extracting portion 26, the segment extracting portion 282calculates angles α made by segments SB comprised in the sectional shapedata DK and the normal line HS of the standard surface RM or thestandard line RS. The segments extracting portion 282 then judgeswhether or not each of the calculated angles a is in the inclinationangle range θ±δ to extract segments SB in the allowable range.

[0063] The noise eliminating portion 283 eliminates a polygon PG or asegment SB that does not consecutive, or isolate, from the extractedpolygons PG or segments SB as noise. Algorithm for eliminating the noiseis as follows, for example.

[0064] In the case where two or more polygons PG are consecutive in theextracted polygons PG, such polygons PG are extracted as normal polygonsPG. Also, polygon data MR are divided into areas each having apredetermined size, and it is judged whether or not a percentage of theextracted polygons PG present in the predetermined area are higher thana predetermined percentage. In the case where the extracted polygons PGare present in a percentage higher than the predetermined percentage inthe predetermined area, a surface composed of the polygons PG isextracted as a normal surface T. For example, an area wherein apredetermined number of polygons PG exist is designated as thepredetermined area. In this case, size of the area may be changed byarbitrarily changing the predetermined number.

[0065] In turn, in the case where two or more segments SB areconsecutive, such segments SB are set as normal segments SB. Also,sectional shape data are divided into areas each having a predeterminedsize, and it is judged whether or not a percentage of the extractedsegments SB present in the predetermined area is higher than apredetermined percentage. In the case where the extracted segments SBare present in a percentage higher than the predetermined percentage inthe predetermined area, the segments SB are extracted as a normalsegment U. For example, an area wherein a predetermined number ofsegments SB exist is designated as the predetermined area. In this case,size of the area may be changed by arbitrarily changing thepredetermined number.

[0066] The sorting and grouping portion 29 performs sorting by setting apolygon PG or polygons PG extracted correspondingly to one of the setinclination angles θ as belonging to an identical group. The sorting maybe performed by, for example, setting neighboring or consecutivepolygons PG as a group and non-consecutive polygons PG as another group.

[0067] Also, the sorting may be performed in such a manner by dividingan extracted surface T into predetermined areas, and setting extractedpolygons PG as a group when the extracted polygons PG are contained inone of the predetermined areas of the extracted surface T in apredetermined percentage and values of intercepts of the polygons PG arein a predetermined range. Here, the intercept is represented by d in thefollowing equation:

a·xo+b·yo+c·zo=d,

[0068] provided that

a(x−xo)+b(y−yo)+c(z−zo)=0.

[0069] The sorting and grouping portion 29 sorts the segments SBextracted by the extracting portion 28 by directions. More specifically,the segments SB extracted correspondingly to one of the set inclinationangles θ are set as a group.

[0070] The display processing portion 30 displays the extracted surfacesT. In this case, each of the surfaces T is displayed as being put acolor or a pattern designated by the color designating portion 24. Thedisplay processing portion 30 displays only the surfaces T designated bythe selection designating portion 25.

[0071] The surfaces T1 to T3 shown in FIG. 6 are extracted by setting aninclination angle θ as 0 degree (i.e. in parallel) with respect to thestandard surface RM shown in FIG. 5. The surfaces T1 to T3 are parallelto the standard surface RM and the surface T1 is reverse to the surfacesT2 and T3.

[0072] In this case, the surfaces T1 to T3 are displayed with being putan identical color such as blue, in the image HG3. If it is set thatcolors of back side and front side are displayed by different colors, T1is put a color different from that of T2 and T3 (T2 and T3 are put thesame color). Further, if it is set that groups are displayed bydifferent colors, different colors are put to the surfaces T1 to T3.

[0073] The surfaces T1 to T8 shown in FIG. 7 are extracted when theinclination angle θ is set as 90 degrees (i.e. perpendicular) withrespect to the standard surface RM shown in FIG. 5. The surfaces T1 toT8 are perpendicular to the standard surface RM.

[0074] In this case, the surfaces T1 to T8 are shown by an identicalcolor such as green in the image HG4. If it is set that colors of groupsare different to each other, different colors are put to the surfaces T1to T8.

[0075] It is possible to display the surfaces T1 to T3 shown in FIG. 6and the surfaces T1 to T8 shown in FIG. 7 with putting colorssimultaneously to them. In this case, it is also possible to assign anarbitrary surface T to be displayed or not to be displayed by using thecolor designating portion 24 or the selection designating portion 25.

[0076] Thus, a user can easily understand a condition and a shape of theobject Q by displaying extracted surfaces T with putting them variouscolors or patterns.

[0077] In the polygon data MR shown in FIG. 6 or 7, one of the extractedsurfaces T is designated so that distances between the standard surfaceRM and the designated surfaces T or distances between each of thedesignated surfaces T are automatically calculated. The calculateddistances are displayed as sizes of parts of the object Q as the imageHG5 shown FIG. 8.

[0078] In this case, it is possible to display only a distance of anormal surface by pointing the normal surface T by using the mouse 14.

[0079] In the example shown in FIG. 13, the lines U1 to U6 extractedwhen the inclination angle θ is set to be 90 degrees (i.e.perpendicular) with respect to the standard line RS are displayed.

[0080] In this case, the extracted lines U1 to U6 are displayed by thesame color in the image HG7, and other lines are displayed in adifferent color. If it is set that groups are different in color, thelines U1 to U6 are displayed by different colors.

[0081] In FIG. 11, the white polygon PG1 to PG10 are the extractedsurfaces T, and the black polygons PG11 to PG14 are the non-extractedsurfaces. The extracted polygon PG10 is surrounded by the polygons PG11to PG13 each of which is not extracted. In this case, thenon-consecutive polygon PG10 is eliminated as noise, and the consecutivepolygons PG1 to pg9 are regarded as normal polygons PG (surface T).

[0082] As described above, it is judged whether or not the extractedsurface is noise, and the surfaces T judged to be noises are eliminated.

[0083] Further, in the case of the sectional shape data DK, the segmentS in a circle, SE1 and SE2 are eliminated as noise since they arenon-consecutive as shown in FIG. 15.

[0084] A flow of processing carried out by the data processing apparatus1 will be described below with reference to the flowchart shown in FIG.16.

[0085] In FIG. 16, three-dimensional shape data DT are input to bememorized in a memory area AR1 (#11). Sectional shape data DK aregenerated as required (#12). A standard surface RM and a standard lineRS are set (#13). An inclination angle θ and an allowable angle δ areset or assigned (#14).

[0086] Then, angles of polygons PG or of segments SB with respect to thestandard surface RM or the standard line RS are calculated (#15). Thereare extracted polygons PG and segments SB that are in an inclinationangle range θ±δ from the polygons PG and segments SB (#16). Noise iseliminated from the extracted polygons PG and segments SB (#17).

[0087] The extracted polygons PG and segments SB are sorted into groupswhen so required (#18). The polygons PG and the segments SB aredisplayed with being designated colors or patters (#19). The polygons PGand the segments SB are printed out when so required. The extractedpolygons PG, the extracted segments SB, the generated three-dimensionalshape data DT, sectional shape data DK and the like are memorized in therecording area AR2 to be stored. The stored date are memorized in therecording media MA1 and MA2 and taken out therefrom as required, andtransferred to an external device via an appropriate interface or toanother computer via a network such as the Internet.

[0088] Thus, it is possible to easily extract surfaces or linesstructuring an outline of an object Q from three-dimensional shape dataDT or sectional shape data DK of the object Q.

[0089] Further, visibility of the three-dimensional shape data DT isimproved by displaying with putting a color or pattern to each of theextracted surfaces or displaying the extracted surfaces by sorting theminto groups and putting different colors or patters to the groups. Thus,understanding of the object Q is remarkably facilitated.

[0090] Moreover, the object Q can be easily examined by calculatingsizes between surfaces or between a surface and a line and displayingthem. It is possible to automate the examination of the object Q bycomparing the calculated sizes with design values.

[0091] It is possible to examine the object with confirming a structureof an arbitrary cross-section of the object Q by displaying thesectional shape data DK or by displaying the lines or sizes extracted byusing the sectional shape data DK.

[0092] In the embodiments described above, it is possible to use alaptop-type personal computer, a desk top-type personal computer, anote-type personal computer, a palm top-type personal computer or othervarious types of personal computers or workstation as the dataprocessing apparatus. Further, it is possible to modify whole or part ofthe data processing apparatus, processing contents, processing order,contents of images to be displayed, display method and the likeaccording to the spirit and scope of the present invention. The presentinvention may be used for various objects including goods, assemblyparts, living creatures and so on.

What is claimed is:
 1. A method for extracting a surface fromthree-dimensional shape data, comprising: setting a standard surface ora standard line with respect to three-dimensional shape data comprisingpolygons representing an object in a space where the three-dimensionalshape data exist; extracting from the three-dimensional shape datapolygons each having an inclination angle in a predetermined range withrespect to the set standard surface or the set standard line; andsetting a collection of the extracted polygons as an extracted surface.2. A method for extracting a surface from three-dimensional shape datacomprising: setting a standard surface or a standard line with respectto three-dimensional shape data comprising polygons representing anobject in a space where the three-dimensional shape data exist; settinginclination angles of the polygons with respect to the set standardsurface or the set standard line; designating an allowable range in theset inclination angles; calculating angles made by the polygons and thestandard surface or the standard line; and extracting a polygon of whichthe calculated angle is in the allowable range of the inclinationangles.
 3. An apparatus for extracting a surface from three-dimensionalshape data comprising: a setting portion for setting a standard surfaceor a standard line with respect to three-dimensional shape datacomprising polygons representing an object in a space where thethree-dimensional shape data exist; an angle setting portion for settinginclination angles of the polygons with respect the set standard surfaceor the set standard line; an designating portion for designating anallowable range in the set inclination angles; a calculating portion forcalculating angles made by the polygons and the standard surface or thestandard line; and an extracting portion for extracting a polygon ofwhich the calculated angle is in the allowable range of the inclinationangles.
 4. An apparatus for extracting a surface from three-dimensionalshape data comprising: a setting portion for setting a standard surfaceor a standard line with respect to three-dimensional shape datacomprising polygons representing an object in a space where thethree-dimensional shape data exist; a standard element calculatingportion for setting a standard element that is a surface or a linehaving a specific relationship with the set standard surface or thepolygons; an angle setting portion for setting inclination angles of thepolygons with respect to the set standard surface or the set standardline; a designating portion for designating an allowable range in theset inclination angles; a calculating portion for calculating anglesmade by the polygons and the standard surface or the standard line; andan extracting portion for extracting a polygon of which the calculatedangle is in the allowable range of the inclination angle.
 5. Theapparatus for extracting a surface from three-dimensional data accordingto claim 4, comprising a noise eliminating portion for extracting asurface as a normal surface only when the surface is composed of theextracted polygons wherein two or more polygons are consecutive or ofthe extracted polygons that are present in a predetermined area in apercentage higher than a predetermined percentage.
 6. The apparatus forextracting a surface from three-dimensional data according to claim 4,comprising: a cross-section extracting portion for calculating, based onthe three-dimensional shape data, sectional shape data comprising acollection of segments and indicating a sectional shape of the object; acalculating portion for calculating angles made by each of thecollection of segments and the standard element of the standard surfaceor the standard line; and an extracting portion for extracting a segmentwhose angle obtained by the calculation is in the allowable range of theset inclination angles.
 7. The apparatus for extracting a surface fromthree-dimensional shape data according to claim 4, wherein the standardelement is a normal line.
 8. The apparatus for extracting a surface fromthree-dimensional shape data according to claim 4, comprising a displayprocessing portion for displaying each collection of extracted polygonson a display as a surface and displaying a collection of polygonsextracted correspondingly to one of the inclination angles with puttingthereto a color or a pattern that is different from colors or patternsof other collections of polygons.
 9. The apparatus for extracting asurface from three-dimensional shape data according to claim 4,comprising a sorting and grouping portion for sorting the polygonsextracted correspondingly to the inclination angles into groupsdepending on the inclination angles.
 10. The apparatus for extracting asurface from three-dimensional shape data according to claim 4,comprising a display processing portion for displaying each collectionof extracted polygons on a display as a surface and displaying acollection of polygons extracted correspondingly to one of theinclination angles with putting thereto a color or a pattern that isdifferent from colors or patterns of other collections of polygons. 11.The apparatus for extracting a surface from three-dimensional shape dataaccording to claim 4, comprising a display processing portion fordisplaying each collection of extracted polygons on a display as asurface and for displaying surfaces that are in parallel to each otherwith putting to their back sides a color or a pattern that is differentfrom a color or a pattern of their front sides.
 12. The apparatus forextracting a surface from three-dimensional shape data according toclaim 4, comprising a calculating portion for calculating a distancebetween a surface comprising the collection of extracted polygons andthe standard surface.
 13. An apparatus for processing three-dimensionalshape data comprising: a calculating portion for calculating, based onthree-dimensional shape data comprising polygons representing an object,sectional shape data comprising a collection of segments and indicatinga sectional shape of the object; a setting portion for setting astandard surface or a standard line in a space wherein thethree-dimensional shape data exist; a standard element calculatingportion for determining a standard element that is a surface or a linehaving a specific positional relationship with the set standard surface;an angle setting portion for setting inclination angles of polygons withrespect to the standard element of the standard surface or the standardline; an designating portion for designating an allowable range in theset inclination angles; a calculation portion for calculating anglesmade by the segments and the standard element of the standard surface orthe standard line; and an extracting portion for extracting a segmentwhose angle obtained by the calculation is in the allowable range ofinclination angles.
 14. A computer-readable recording medium wherein aprogram is recorded, the program letting a computer perform theprocessing of: setting a standard surface or a standard line withrespect to three-dimensional shape data comprising polygons representingan object in a space wherein the three-dimensional shape data exist;extracting from the three-dimensional shape data polygons whoseinclination angles with respect to the set standard surface or the setstandard line are in a predetermined range; and setting a collection ofthe extracted polygons as a surface.
 15. A computer-readable recordingmedium wherein a program is recorded, the program letting a computerperform the processing of: setting a standard surface or a standard linewith respect to three-dimensional shape data comprising polygonsrepresenting an object in a space wherein the three-dimensional shapedata exist; determining a standard element that is a surface or a linehaving a specific positional relationship with the set standard surfaceor the polygons; setting inclination angles of polygons with respect tothe standard element of the set standard surface or the set standardline; designating an allowable range in the set inclination angles;calculating angles made by the polygons and the standard surface or thestandard line; extracting a polygon of which the calculated angle is inthe allowable range of the inclination angles; and displaying acollection of the extracted polygons as a surface.